A035204 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 22.

1, 1, 2, 1, 0, 2, 2, 1, 3, 0, 1, 2, 2, 2, 0, 1, 0, 3, 0, 0, 4, 1, 0, 2, 1, 2, 4, 2, 2, 0, 0, 1, 2, 0, 0, 3, 0, 0, 4, 0, 0, 4, 0, 1, 0, 0, 0, 2, 3, 1, 0, 2, 0, 4, 0, 2, 0, 2, 2, 0, 2, 0, 6, 1, 0, 2, 2, 0, 0, 0, 0, 3, 0, 0, 2, 0, 2, 4, 2, 0, 5

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

From Amiram Eldar, Nov 19 2023: (Start)

a(n) = Sum_{d|n} Kronecker(22, d).

Multiplicative with a(p^e) = 1 if Kronecker(22, p) = 0 (p = 2 or 11), a(p^e) = (1+(-1)^e)/2 if Kronecker(22, p) = -1 (p is in A038896), and a(p^e) = e+1 if Kronecker(22, p) = 1 (p is in A038895 \ {2, 11}).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log(42*sqrt(22)+197)/sqrt(22) = 1.274160921644... . (End)

Mathematica

a[n_] := DivisorSum[n, KroneckerSymbol[22, #] &]; Array[a, 100] (* Amiram Eldar, Nov 19 2023 *)

Prog

(PARI) my(m = 22); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(22, d)); \\ Amiram Eldar, Nov 19 2023

Crossrefs

Cf. A038895, A038896.

Sequence in context: A198727 A294508 A035152 * A349621 A326987 A190775

Adjacent sequences: A035201 A035202 A035203 * A035205 A035206 A035207

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved